I appreciate the comments, guys.
I'll be shooting at 50, then 100 yards. They bore-sighted it at the hardware store when they installed the scope and mounts... That should get it on the paper at 50yds.
I'll bring the gun vice with me. After I fire the first shot, I'll put the rifle in the vice and point the crosshairs on the bullet hole, wherever it is. Then with it firmly held in the vice, I'll adjust the scope and move the crosshairs to where I want it to shoot at 50yd, just above the bullseye. In theory, this should get it sighted at 50yd with one shot. - I'll fire another round at 50yd to be sure, then move over to the 100yd target.
The gun vice is only necessary for the scope adjustment... After the adjustment I'll go back to the sandbags for shooting, and the gun vise will go back to the trunk of the car to keep it out of the way.
I'll be cooling and cleaning the barrel between each shot at first, so it will be slow going. The barrel break-in regime I'm following calls for cleaning between each shot for the first ten shots, then between every five shots for a while, then finally I can just clean it every ten or twenty rounds thereafter.
Almost all rounds fired through this rifle will be off of the bench. - Personally I am a big-bore enthusiast, but I wanted something good for family shooting outings, accurate and light recoiling off of the bench that could still reasonably be used for a deer, hog or varmint hunt should the occasion arise. Originally it was going to be in .250 Savage, but in the end I opted for .243 for easy ammo availability, even though it probably kicks a bit more than the .250 Savage would.
If recoil is still an issue with this rifle, I'll send it off to Magna-Port. - But hopefully that will not be necessary. Magna-Porting did wonders for my Browning A-bolt SS in .300 Win mag, and it had no effect upon accuracy or even the scope adjustment!
Everybody in the family likes to shoot, but nobody besides myself likes to shoot any of the big-bore stuff.

Right now the only ceterfire I have that the wife and kids like to shoot is a collectible Swedish Mauser I am hanging onto, but I feel like mounting a scope or receiver sight on the old Mauser would be a travesty and that's what led me to have this rifle made up.
At this location the .17HMR is good for 1/4" groups at 50yd, but at 100yd it is not unusual to see 4" horizontal stringing on account of the wind. I'll probably use the 17 to try to learn to dope the wind with, as the results are so easy to see with it... It's reasonably cheap to shoot, too! That is an important factor as I am a slow learner and will pop off quite a few rounds trying to get it worked out.